Ex 12.2, 3
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman s time.
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
Let number of tennis racket be x
number of cricket bats be y
According to Question :
As we want Maximize the profit.
Hence the function used here will be Maximize Z
Profit on each tennis racket Rs 20
Profit on each Cricket Bat Rs 10
Max Z = 20x + 10y
Combining all the constraints :
Maximize Z = 20x + 10y
Subject to constraints,
x + 2y 28
3x + y 24
x 0, y 0
Thus,
4 tennis Rackets and 12 cricket bats must be made so that factory runs at full capacity.
Maximum Profit is Rs 200, when 4 tennis bats and 2 cricket bats are Produced.